Question

simplify and factorise

Answer 1

Answer:

= 4(b + c)(a + b – c)

Step-by-step explanation:

let (a+b+c)2 – (a – b – c)2+ 4b2– 4c2

= a2 + b2 + c2 + 2ab + 2bc + 2ca – (a2 + b2 + c2 – 2ab + 2bc – 2ca)+ 4b2– 4c2

= a2 + b2 + c2 + 2ab + 2bc + 2ca – a2 – b2 – c2 + 2ab – 2bc +2ca + 4b2– 4c2

= 4ab + 4ca + 4b2– 4c2

= 4(ab + ca + b2– c2)

= 4[a(b + c) +(b2– c2)]

= 4[a(b + c) + (b + c)(b – c)]

= 4(b + c)(a + b – c)

(answer)